Thread: Determining plane based on lines in R^3

1. Determining plane based on lines in R^3

For the question below, what is the strategy for determining the position and direction vectors of the plane P? In order to derive the 2 direction vectors, I would need to know 3 points on the plane, and then compute the difference. The points can be determined by evaluating either line A or line B at some point t. I'm not sure which points to use however. Help?

As for the position vector, I think this will rely on how I determine the direction vectors. I also need help with this.

2. Re: Determining plane based on lines in R^3 Originally Posted by otownsend For the question below, what is the strategy for determining the position and direction vectors of the plane P? In order to derive the 2 direction vectors, I would need to know 3 points on the plane, and then compute the difference. The points can be determined by evaluating either line A or line B at some point t. I'm not sure which points to use however. Help?
As for the position vector, I think this will rely on how I determine the direction vectors. I also need help with this.
First we need to know that the lines intersect: $(0,0,1)\in\ell_1(t)\cap\ell_2(s)$
$\left<1,2,3,\right>$ is the direction vector of $\ell_1(t)$ and $\left<-1,1,1,\right>$ is the direction vector of $\ell_2(s)$
The normal to the plane is $\left<1,2,3,\right>\times\left<-1,1,1\right>$
You have a point and a normal write the equation of the plane.

3. Re: Determining plane based on lines in R^3

Nvm. Thank you for your help!

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